Eevee finds its origins in generic members of the order Carnivora, among them cats, dogs, and most mammalian carnivores. In the end, Eevee just resembles the basic small carnivorous mammal blueprint, evolves into more specific forms (from the dog like Flareon to the cat-like Espeon). As such, Eevee may be based of Miacids, the ancestors of all modern carnivorans (dogs cats hyenas bears viverids mustelids skunks racoons).

Origin
Eevee shares traits with foxes, more specifically the Fennec fox, dogs and cats. It is possibly based on the folklore of Tanuki (Nyctereutes procyonoides viverrinus), who is said to be able to transform and is the alternative name for the Japanese raccoon dog.
It may also be based on the concept of dog breeding and the multitude of variations that arose from it. It may also be based on the fox's ability to adapt to extreme environments, like the desert fox and the arctic fox.
Note: I took this from bulbapedia. Every Pokemon on bulbapedia has at the bottom a section called origin.